Finite Group Databasebeta

← #21455361

Subgroups — #21455361

Order 7808.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C2×#14519800C211yesmaximal, characteristic, complemented
3#16840330C211yesmaximal, characteristic, complemented
4#16840244C211yesmaximal, characteristic, complemented
5#16839986C211yesmaximal, characteristic, complemented
6#16839980C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839962C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839958C211yesmaximal, characteristic, complemented
11#16839956C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519804—24no—
20#14519800—24no—
21C2×#11758201C2211yescharacteristic
22C2×#11758201C2211yescharacteristic, complemented
23C2×#11758201C2211yescharacteristic, complemented
24C2×D488C2211yescharacteristic
25C2×D488C2211yescharacteristic, complemented
26C2×#11758199C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519774C2211yescharacteristic
30#14519773C2211yescharacteristic
31#14519766C2211yescharacteristic
32#14519750—21no—
33#14519750—21no—
34#14519747—21no—
35#14519747—21no—
36Q8×Dic61C2211yescharacteristic, complemented
37C4×D244—21no—
38C4×D244C2211yescharacteristic, complemented
39#14519739—21no—
40#14519739C2211yescharacteristic, complemented
41#14519734—21no—
42#14519734C2211yescharacteristic
43C4⋊C4×D61—21no—
44C4⋊C4×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic, complemented
46#14519706C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic
52#14519697C2211yescharacteristic
53#14519697C2211yescharacteristic, complemented
54C2×Q16×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68#11758226—22no—
69#11758226—22no—
70#11758226—22no—
71#11758226D414yescomplemented
72D4×D61—22no—
73D4×D61—22no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61C2311yescharacteristic
87Q16×C61—22no—
88SD16×C61—22no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C42×C61—21no—
96C42×C61C2311yescharacteristic
97#11758201—22no—
98#11758201—22no—
99#11758201—22no—
100#11758199—22no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198D411yescharacteristic
106#11758198D411yescharacteristic
107C4⋊Dic61—21no—
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196D411yescharacteristic
111#11758196D411yescharacteristic
112C4×Dic61—21no—
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116D488—22no—
117D488—22no—
118#11758189—22no—
119C8×D61—22no—
120C23×C61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—42no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61C2×D411yescharacteristic
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61C2×D412yes—
132D4×C61—21no—
133D4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—81no—
142C22⋊D61—81no—
143C2×Dic61—21no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—24no—
148D244—21no—
149D244—21no—
150D244—21no—
151D244—21no—
152D244—21no—
153D244—42no—
154D244—81no—
155D244—81no—
156D244C2×D412yes—
157C4×D61—24no—
158C4×D61—42no—
159C4×D61—81no—
160C4×D61—81no—
161C4×D61—81no—
162C4×D61C2×D412yes—
163C4×D61#4112yes—
164C8×C61—21no—
165C8×C61—21no—
166#92418—21no—
167#92418—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—22no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—84no—
184C2×D61#12112yes—
185C4×C61—22no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61C22×D411yescharacteristic
191C4×C61C2×#4111yescharacteristic
192Dic61—21no—
193Dic61—21no—
194Dic61—41no—
195Dic61#12112yes—
196#3045—611nomaximal, Sylow
197C2×C61—81no—
198C2×C61C2×#12111yescharacteristic
199C2×C61#57611yescharacteristic
200C2×C61#57711yescharacteristic
201D61—22no—
202D61—42no—
203D61—81no—
204D61—81no—
205C2×AGL(1,ℤ/8)—611no—
206C2×#135—611no—
207#535—611no—
208#520—611no—
209#464—611no—
210#464D6111yescharacteristic, complemented
211#463—611no—
212#463—611no—
213#460—611no—
214#460—611no—
215#459—611no—
216#459—611no—
217#424—611no—
218#417—611no—
219C2×#102—611no—
220C61#304511yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C2×#41—611no—
223C22×D4—611no—
224AGL(1,ℤ/8)—1224no—
225#135—1224no—
226C2×Q16C2×D6111yescharacteristic, complemented
227C2×SD16—611no—
228C2×SD16—611no—
229C2×SD16—611no—
230C2×SD16C2×D6111yescharacteristic
231C2×D8—611no—
232C2×D8—611no—
233C2×D8—611no—
234C2×M16—611no—
235C22×C8—611no—
236#127—611no—
237#127—611no—
238#124—611no—
239#124C2×D6111yescharacteristic
240#121—1221no—
241#121—1221no—
242#120—1221no—
243#120—1221no—
244C4×Q8—611no—
245C4×Q8C2×D6111yescharacteristic, complemented
246C4×D4—611no—
247C4×D4—611no—
248C4×D4—1221no—
249C4×D4—1221no—
250#117—611no—
251#117—1221no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1221no—
254C4⋊C8—611no—
255C4⋊C8—611no—
256C4⋊C8—611no—
257C4⋊C8C2×D6111yescharacteristic, complemented
258#103—611no—
259#103C2×D6111yescharacteristic, complemented
260#102—611no—
261#102—611no—
262#102—611no—
263#102—611no—
264#102—611no—
265#102C2×D6111yescharacteristic
266C24—1221no—
267#41—614no—
268#41—1222no—
269#41—1222no—
270#41—1222no—
271C2×Q8C22×D6111yescharacteristic
272C2×Q8C22×D6111yescharacteristic
273C2×D4—611no—
274C2×D4—611no—
275C2×D4—611no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1222no—
279C2×D4—1222no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4C22×D6111yescharacteristic
286C22×C4—611no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292Q16—22no—
293SD16—22no—
294SD16—1222no—
295SD16—1222no—
296SD16—1222no—
297D8—1222no—
298D8—1222no—
299D8—1222no—
300M16—1222no—
301C2×C8—611no—
302C2×C8—611no—
303C2×C8—1222no—
304C2×C8C22×D6111yescharacteristic
305C2×C8C22×D6111yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—611no—
308C4⋊C4—611no—
309C4⋊C4—611no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4C22×D6111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—611no—
316C22⋊C4—611no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C42—21no—
322C42—611no—
323C42—1221no—
324C42C22×D6111yescharacteristic
325C23—21no—
326C23—611no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—4881no—
331C23—4881no—
332C23—2442no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8D4×D6112yes—
337D4—21no—
338D4—21no—
339D4—612no—
340D4—1224no—
341D4—1221no—
342D4—1221no—
343D4—1221no—
344D4—1221no—
345D4—1221no—
346D4—4881no—
347D4—4881no—
348D4—4881no—
349D4—4881no—
350D4—2442no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—611no—
356C2×C4—612no—
357C2×C4—612no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—1224no—
361C2×C4—1221no—
362C2×C4—4881no—
363C2×C4—4881no—
364C2×C4—4881no—
365C2×C4—2442no—
366C2×C4D4×D6111yescharacteristic
367C2×C4D4×D6111yescharacteristic
368C2×C4C23×D6111yescharacteristic
369C8—21no—
370C8—21no—
371C8—1221no—
372C8—1221no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—612no—
377C22—1221no—
378C22—1221no—
379C22—1222no—
380C22—4884no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22C2×D4×D6111yescharacteristic
390C4—22no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—612no—
396C4—1221no—
397C4—1221no—
398C4—2441no—
399C4C2×D4×D6111yescharacteristic
400C4#41×D6111yescharacteristic
401C2—81no—
402C2—1222no—
403C2—4881no—
404C2—4881no—
405C2—2442no—
406C2#121×D6111yescharacteristic
407C2#1684056411yescharacteristic
408C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3045
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×#14519800C2semidirect
3. #16840330C2semidirect
4. #16840244C2semidirect
5. #16839986C2semidirect
6. #16839980C2semidirect
7. #16839974C2semidirect
8. #16839962C2semidirect
9. #16839960C2semidirect
10. #16839958C2semidirect
11. #16839956C2semidirect
12. #16839787C2semidirect
13. #16839762C2semidirect
14. #102×D61C2semidirect
15. C61×#464C2semidirect
22. C2×#11758201C22semidirect
23. C2×#11758201C22semidirect
25. C2×D488C22semidirect
36. Q8×Dic61C22semidirect
38. C4×D244C22semidirect
40. #14519739C22semidirect
45. C4⋊#92418C22semidirect
46. #14519706C22semidirect
47. #14519706C22semidirect
48. #14519701C22semidirect
50. #14519699C22semidirect
53. #14519697C22semidirect
54. C2×Q16×C61C22semidirect
57. C4×Q8×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
71. #11758226D4semidirect
210. #464D61semidirect
220. C61#3045semidirect
226. C2×Q16C2×D61semidirect
245. C4×Q8C2×D61semidirect
257. C4⋊C8C2×D61semidirect
259. #103C2×D61semidirect